1. Related Rates
2.7

2. Steps for Related Rates Problems:
Finding a rate of change that cannot be easily measured by using another rate that can be is called a Related Rate problem.
Steps for Related Rates Problems:
1. Draw a picture (sketch).
2. Write down known information.
3. Write down what you are looking for.
4. Write an equation to relate the variables.
5. Differentiate both sides with respect to t.
6. Evaluate.

3. y = 8 by Pythagorean theorem
A ladder, 10 ft tall rests against a wall. If the ladder is sliding away from the bottom of the wall at 1 ft/sec, how fast is the top of the ladder coming down the wall when the bottom is 6 ft from the wall?
We want dy/dt when x = 6 10 y x
The ladder is moving down the wall at ¾ ft/sec when it is 6 ft. from the wall.
At x = 6,
y = 8 by Pythagorean theorem

4. Water is draining from a cylindrical tank at 3 liters/second
Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping?
Find
(We need a formula to relate V and h. )
(r is a constant.)

5. Hot Air Balloon Problem:
Given:
How fast is the balloon rising?
Find

6. Hot Air Balloon Problem:
Given:
How fast is the balloon rising?
Find

7. We want dr/dt when d=50 or r = 25
Air is being pumped into a balloon at a rate of 100 cubic cm /sec. How fast is the radius of the balloon increasing when the diameter is 50 cm?
We want dr/dt when d=50 or r = 25

8. Batman and Scooby Doo are having lunch together when they both simultaneously receive a call. Batman heads off to Gotham city traveling east at 40 miles per hour. Scooby hops in the mystery machine and heads north at 30 miles an hour. How fast is the distance between them changing 6 minutes later?

9. The batmobile travels east at 40 mi/hr.
The mystery machine travels north at 30 mi/hr.
How fast is the distance between the vehicles changing 6 minutes later? B A

10. Batman travels east at 40 mi/hr. Scooby travels north at 30 mi/hr.
How fast is the distance between the vehicles changing 6 minutes later? B A